Starting with polynomial:
P : t
Extension levels are: 1 18 34
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : t^19 - 171*t^17 + 11628*t^15 - 406980*t^13 + 7936110*t^11 - 87297210*t^9 + 523783260*t^7 - 1571349780*t^5 + 1964187225*t^3 - 654729075*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^53 - 3061558570264471841290086093/2901478992069837568667224*t^51 + 34245045036362413294206051748257/66734016817606264079346152*t^49 - 2550793581889149410320086405680715/16683504204401566019836538*t^47 + 5742742771462797905442810989924313423/183518546248417226218201918*t^45 - 1716171089839142163170187022457340205845/367037092496834452436403836*t^43 + 194233306930768866606081325276853440957455/367037092496834452436403836*t^41 - 8525672266160762432011871199700439140326105/183518546248417226218201918*t^39 + 589752753844179602406613796809413977793367125/183518546248417226218201918*t^37 - 129914727437406066531179924655820607341149752895/734074184993668904872807672*t^35 + 5732345342914398176316605189421649572473135617725/734074184993668904872807672*t^33 - 2310319303532782456262836129397530189105533099075/8341752102200783009918269*t^31 + 65902304717862937085229252712915409284693221334125/8341752102200783009918269*t^29 - 3018472192386422892444019090328390785862352258428625/16683504204401566019836538*t^27 + 55270097716911525783999693288999130924991399370667875/16683504204401566019836538*t^25 - 17476889799790052040182048485677058651436833249145625/362684874008729696083403*t^23 + 200110365044135425773522961965015202268925936203835000/362684874008729696083403*t^21 - 14254894398666081509189195140070506702821007612895461875/2901478992069837568667224*t^19 + 97158373279936068445288693612391638306610847319790165625/2901478992069837568667224*t^17 - 124134321167117758996018943408813616751411600446773375625/725369748017459392166806*t^15 + 462992392014303719803304337214155990289596110198204859375/725369748017459392166806*t^13 - 2431020997524255459436667022300999137919186456329329115625/1450739496034918784333612*t^11 + 4273425772336798009962415905194918823327415652895433396875/1450739496034918784333612*t^9 - 2338896500065506578317923636764936318046033072351344390625/725369748017459392166806*t^7 + 1422303688780182091304639767531085538933057287919757190625/725369748017459392166806*t^5 - 1566264147545049139003701534683433249400076724271151203125/2901478992069837568667224*t^3 + 121511881694425137006077550374778177431334247812912609375/2901478992069837568667224*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-2.5291688318535963483 + 1.321398832050183148e-953j)  +/-  (1.78e-247, 1.78e-247j)
| (9.7355175902564015511 + 1.0378069726442002363e-950j)  +/-  (7.45e-244, 7.45e-244j)
| (12.167185730082901481 + 3.3534660341706892929e-954j)  +/-  (1.5e-246, 1.5e-246j)
| (8.4845430768020301477 - 1.4743094455160749508e-949j)  +/-  (5.15e-243, 5.15e-243j)
| (-11.22055771989146376 - 3.2168671471923530056e-949j)  +/-  (2.42e-245, 2.42e-245j)
| (-7.3825790240304318677 + 1.593467717238229666e-955j)  +/-  (2.2e-242, 2.2e-242j)
| (-10.435995494721377627 - 8.2591145646959775899e-975j)  +/-  (1.63e-244, 1.63e-244j)
| (7.3825790240304318677 + 1.6423824305486034094e-983j)  +/-  (2.15e-242, 2.15e-242j)
| (-7.9133502424629457652 - 1.4963775580078657034e-982j)  +/-  (1.05e-242, 1.05e-242j)
| (4.0634670868068548897 - 9.2654202709862775303e-996j)  +/-  (9.11e-245, 9.11e-245j)
| (1.7849504170995194264 + 6.5144357875163588747e-1001j)  +/-  (2.87e-249, 2.87e-249j)
| (2.1555027613169351403 - 1.4559087617415591593e-1000j)  +/-  (2.35e-248, 2.35e-248j)
| (-8.4845430768020301477 - 2.0074848941266461169e-993j)  +/-  (4.91e-243, 4.91e-243j)
| (-2.1555027613169351403 + 1.8324142774666358652e-1001j)  +/-  (2.61e-248, 2.61e-248j)
| (-6.2628911565132517042 + 2.6731758859021647406e-994j)  +/-  (9.9e-243, 9.9e-243j)
| (-12.167185730082901481 + 1.2887755831065415301e-1002j)  +/-  (1.49e-246, 1.49e-246j)
| (-9.7355175902564015511 + 4.6499103226401347478e-1000j)  +/-  (6.38e-244, 6.38e-244j)
| (-9.0897999835173516381 - 3.9075509721471118254e-999j)  +/-  (2.22e-243, 2.22e-243j)
| (10.435995494721377627 + 6.368898028308473696e-1002j)  +/-  (1.58e-244, 1.58e-244j)
| (3.6644165474506384767 + 1.1463509067012403148e-1001j)  +/-  (2.18e-245, 2.18e-245j)
| (-5.3205363773360380316 - 7.9215843493507000128e-998j)  +/-  (1.62e-243, 1.62e-243j)
| (0.34898109544067841238 + 1.1412910572701575908e-1014j)  +/-  (1.05e-253, 1.05e-253j)
| (1.4288766760783728713 + 2.9181423184802372412e-1011j)  +/-  (3.04e-250, 3.04e-250j)
| (-1.7849504170995194264 - 7.0467910143400560383e-1010j)  +/-  (2.9e-249, 2.9e-249j)
| (-1.075942905688036213 + 3.4799811358021501064e-1012j)  +/-  (2.8e-251, 2.8e-251j)
| (5.3205363773360380316 + 3.9092998244129591423e-1005j)  +/-  (1.74e-243, 1.74e-243j)
| (2.8980512765157531201 - 7.7826239645945488181e-1008j)  +/-  (9.63e-247, 9.63e-247j)
| (3.2735765139580508977 - 2.5987461467543442638e-1007j)  +/-  (4.68e-246, 4.68e-246j)
| (-2.8980512765157531201 + 9.1629505284459403228e-1008j)  +/-  (1.1e-246, 1.1e-246j)
| (11.22055771989146376 + 3.3535175453390277541e-1007j)  +/-  (2.29e-245, 2.29e-245j)
| (-4.0634670868068548897 + 4.043587862179255464e-1005j)  +/-  (8.64e-245, 8.64e-245j)
| (-4.8811565860080736303 - 1.2267593165791359762e-1002j)  +/-  (6.84e-244, 6.84e-244j)
| (9.0897999835173516381 + 6.0147031135909068039e-1008j)  +/-  (2.18e-243, 2.18e-243j)
| (4.8811565860080736303 + 2.1899042318286475802e-1007j)  +/-  (7.66e-244, 7.66e-244j)
| (-5.7840228828589062888 - 4.6509380674091758176e-1005j)  +/-  (4.01e-243, 4.01e-243j)
| (7.9133502424629457652 + 2.9122020183644951931e-1016j)  +/-  (1.11e-242, 1.11e-242j)
| (-4.4658726268310313362 - 2.0216819588939556137e-1015j)  +/-  (2.56e-244, 2.56e-244j)
| (1.075942905688036213 - 9.381091533136673218e-1027j)  +/-  (2.84e-251, 2.84e-251j)
| (0.71208504404237994041 - 1.1940553190796621177e-1027j)  +/-  (1.68e-252, 1.68e-252j)
| (2.5291688318535963483 + 4.8691592062521999842e-1022j)  +/-  (2e-247, 2e-247j)
| (-3.2735765139580508977 + 7.8961422198372966351e-1022j)  +/-  (4.68e-246, 4.68e-246j)
| (6.9879074972008547806 + 2.7505488765657538944e-1016j)  +/-  (3.54e-242, 3.54e-242j)
| (6.2628911565132517042 - 1.3345372943548539708e-1017j)  +/-  (1.04e-242, 1.04e-242j)
| (6.7160500194514282878 - 2.9968724031054453703e-1018j)  +/-  (3.37e-242, 3.37e-242j)
| (4.4658726268310313362 - 1.5691149081369728817e-1022j)  +/-  (2.8e-244, 2.8e-244j)
| (-3.6644165474506384767 - 1.995908315162464902e-1020j)  +/-  (2.16e-245, 2.16e-245j)
| (-1.4288766760783728713 + 9.0395230233378844786e-1036j)  +/-  (3.33e-250, 3.33e-250j)
| (-6.9879074972008547806 - 1.7723710198685370716e-1028j)  +/-  (3.55e-242, 3.55e-242j)
| (5.7840228828589062888 + 2.2219150921149615513e-1058j)  +/-  (3.87e-243, 3.87e-243j)
| (-6.7160500194514282878 + 4.8346830499996892668e-1073j)  +/-  (3.05e-242, 3.05e-242j)
| (-0.71208504404237994041 + 6.4345624848355516323e-1089j)  +/-  (1.89e-252, 1.89e-252j)
| (-0.34898109544067841238 + 3.5657203421577839804e-1089j)  +/-  (1.05e-253, 1.05e-253j)
| (-2.755007329748820312e-1211 - 3.3500519973364583491e-1211j)  +/-  (2.3e-1209, 2.3e-1209j)
-------------------------------------------------
The weights are:
| (0.0060407778484316729847 + 1.6275253612473440401e-955j)  +/-  (1.25e-33, 2.19e-154j)
| (7.0085342444073185344e-22 - 3.8246996147070032425e-969j)  +/-  (2.26e-64, 3.96e-185j)
| (3.1110349733656305501e-33 + 2.073163562522439938e-976j)  +/-  (1.01e-69, 1.77e-190j)
| (5.4731178126342324057e-17 + 4.7884095432308058045e-965j)  +/-  (1.47e-61, 2.58e-182j)
| (1.543220525994608201e-28 - 2.0486013118321968056e-974j)  +/-  (1.04e-69, 1.82e-190j)
| (2.9007425367916242218e-13 - 6.1073643203973969597e-964j)  +/-  (4.61e-61, 8.08e-182j)
| (6.5771562457494266111e-25 + 3.4026216429981599726e-972j)  +/-  (1.99e-68, 3.48e-189j)
| (2.9007425367916242218e-13 + 6.0105466494221188349e-963j)  +/-  (1.15e-61, 2.01e-182j)
| (5.5788114570148646888e-15 + 1.977706709993456631e-965j)  +/-  (9.02e-63, 1.58e-183j)
| (4.1481349191781961992e-05 + 6.4791332202313378717e-958j)  +/-  (3.16e-51, 5.54e-172j)
| (0.0295079387639997723 + 1.2332127352742999994e-955j)  +/-  (2.2e-36, 3.85e-157j)
| (0.014648069531827789039 - 6.5381991282179227205e-956j)  +/-  (8.28e-40, 1.45e-160j)
| (5.4731178126342324057e-17 - 5.9889151693695746326e-967j)  +/-  (8.62e-65, 1.51e-185j)
| (0.014648069531827789039 - 4.4279285549389525574e-955j)  +/-  (6.11e-42, 1.07e-162j)
| (5.8214727651044575871e-10 + 1.2243475569332873225e-961j)  +/-  (2.13e-60, 3.73e-181j)
| (3.1110349733656305501e-33 + 3.2224495600786408647e-977j)  +/-  (6.25e-74, 1.09e-194j)
| (7.0085342444073185344e-22 - 2.839899723963434545e-970j)  +/-  (2.56e-68, 4.48e-189j)
| (2.8464764475760547345e-19 + 1.5148884914793989367e-968j)  +/-  (7.34e-67, 1.29e-187j)
| (6.5771562457494266111e-25 + 3.2156325265547503056e-971j)  +/-  (4.9e-74, 8.58e-195j)
| (0.00019209558641393496161 - 2.0428286453990459682e-957j)  +/-  (4.27e-56, 7.48e-177j)
| (1.2861309038260672223e-07 + 5.065335207301203124e-960j)  +/-  (5e-61, 8.76e-182j)
| (0.13377154042747217045 + 5.1632991832955877325e-955j)  +/-  (5.78e-41, 1.01e-161j)
| (0.050402783405252039281 - 2.0705097855801737385e-955j)  +/-  (3.36e-43, 5.89e-164j)
| (0.0295079387639997723 + 4.3061023338535275833e-955j)  +/-  (2.45e-46, 4.29e-167j)
| (0.080120817735734572584 + 5.5019202339992552524e-955j)  +/-  (5.74e-41, 1.01e-161j)
| (1.2861309038260672223e-07 - 9.9792090586777686872e-960j)  +/-  (5.07e-63, 8.89e-184j)
| (0.002211186292480577739 - 1.4948561397447309007e-956j)  +/-  (1.64e-53, 2.87e-174j)
| (0.00072032532647909207365 + 5.9077861496313010274e-957j)  +/-  (5.26e-55, 9.22e-176j)
| (0.002211186292480577739 + 9.48172060339563047e-956j)  +/-  (1.29e-54, 2.27e-175j)
| (1.543220525994608201e-28 - 1.5288137953732844366e-973j)  +/-  (7.34e-77, 1.29e-197j)
| (4.1481349191781961992e-05 - 8.176520447394163342e-958j)  +/-  (6.55e-60, 1.15e-180j)
| (1.1402218472931550079e-06 - 3.1546720180308790853e-959j)  +/-  (7.2e-62, 1.26e-182j)
| (2.8464764475760547345e-19 + 3.7555652082431846097e-967j)  +/-  (8.63e-73, 1.51e-193j)
| (1.1402218472931550079e-06 + 4.6228887788255322885e-959j)  +/-  (6.74e-64, 1.18e-184j)
| (1.026719723935470523e-08 - 7.6034048895871535703e-961j)  +/-  (7.87e-65, 1.38e-185j)
| (5.5788114570148646888e-15 - 4.1849010839494241925e-964j)  +/-  (6.38e-71, 1.12e-191j)
| (7.5689677712743924902e-06 + 1.7082653036248404689e-958j)  +/-  (2.51e-62, 4.4e-183j)
| (0.080120817735734572584 + 3.0029538830322195768e-955j)  +/-  (4.56e-53, 8e-174j)
| (0.11359499683757381488 - 4.0080282118350140159e-955j)  +/-  (1.67e-52, 2.93e-173j)
| (0.0060407778484316729847 + 3.2678353087477915897e-956j)  +/-  (8.05e-58, 1.41e-178j)
| (0.00072032532647909207365 - 1.762818604926544998e-956j)  +/-  (1.84e-60, 3.22e-181j)
| (2.5307407445937601469e-12 - 5.4158802549884153812e-962j)  +/-  (7.81e-70, 1.37e-190j)
| (5.8214727651044575871e-10 - 4.5744635073683965192e-961j)  +/-  (2.27e-69, 3.98e-190j)
| (2.4653567551125657336e-11 + 1.4816554548185829128e-961j)  +/-  (9.36e-70, 1.64e-190j)
| (7.5689677712743924902e-06 - 1.8619201079577328525e-958j)  +/-  (1.05e-65, 1.84e-186j)
| (0.00019209558641393496161 + 3.7527822575242149071e-957j)  +/-  (3.3e-65, 5.78e-186j)
| (0.050402783405252039281 - 4.9732056049198580359e-955j)  +/-  (1.94e-62, 3.4e-183j)
| (2.5307407445937601469e-12 + 8.1604714145874877688e-963j)  +/-  (4.04e-72, 7.09e-193j)
| (1.026719723935470523e-08 + 2.039715273089188201e-960j)  +/-  (4.94e-70, 8.66e-191j)
| (2.4653567551125657336e-11 - 2.8129373396462629776e-962j)  +/-  (1.31e-71, 2.3e-192j)
| (0.11359499683757381488 - 5.853071259070490478e-955j)  +/-  (6.26e-65, 1.11e-185j)
| (0.13377154042747217045 + 6.1805966149930346782e-955j)  +/-  (3.34e-65, 5.66e-186j)
| (0.1374782764312185987 - 6.0526694062978275541e-955j)  +/-  (2.66e-65, 5.25e-186j)
